English

A Geometric Interpretation of the Intertwining Number

Combinatorics 2018-07-09 v1

Abstract

We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining number to the algebraic geometry of Borel orbits. Furthermore, by studying the generating polynomials of our statistics, we determine the q=1q=-1 specialization of a qq-analogue of the Bell numbers. Finally, by using Renner's HH-polynomial of an algebraic monoid, we introduce and study a tt-analog of qq-Stirling numbers.

Keywords

Cite

@article{arxiv.1807.02156,
  title  = {A Geometric Interpretation of the Intertwining Number},
  author = {Mahir Bilen Can and Yonah Cherniavsky and Martin Rubey},
  journal= {arXiv preprint arXiv:1807.02156},
  year   = {2018}
}

Comments

15 pages

R2 v1 2026-06-23T02:52:18.936Z